I'm just genuinely curious about the scientific difference. I'm not tyring to figure out which is better from a Whitmanesque "mystical" point of view. It should go without saying that amazing beautiful pics can be taken with BOTH. That isn't really the core question, imo.
Why would you care about the scientific difference? Isn't the point entirely how it looks? How do you even measure that scientifically? Color gamut? Acutance? Resolution? At how many lp/mm? Zeiss lenses were designed for good micro contrast but worse resolution...is that better or worse and in what contexts? Is grain good or bad? What colors (if any) do you like? How do you feel about false detail (aliasing), is it nice and sharp and crunchy or disgusting to you? Is a lack of DR good or bad? (This is a tricky question--printed images only have four or five stops of contrast at best so a capture with more DR than that looks flat when printed, but one without enough loses detail--the answer is of course subjective and it's based on the subject and light and how the image is developed.)
As a scientific instrument, digital is way better. Astronomers (appropriately enough) switched from film to CCDs in the 1970s and have not looked back. The simple answer here is that digital is WAY better in general.
In terms of signal/noise ratio, digital is just way better. Way, way better. No argument from anyone. But some people like film grain because it looks more random and smooth. The 5D Mark III I have found has pretty ugly noise, imo, while some digital cameras have amazing beautiful noise with a great texture--so that's a whole other subjective discussion.
In terms of resolution it's complicated. Velvia (a very sharp color film) has mtf curves that resolve without aliasing to about 60 or 80 cycles/mm (at like 30% mtf). The D800 has about 200 pixels per mm or 100 cycles/mm. As per the nyquist sampling theorem that means 50 cycles/mm without aliasing and that's not even taking into account bayer interpolation. So it sounds like digital is much worse here, but it's not! Velvia drops off from >100% mtf to <100mtf around 20 cycles/mm but bayer sensors resolve to about 100% mtf until almost 70% of their stated resolution. I think. Without an antialiasing filter, the D800E might resolve 100% mtf (>100% mtf once sharpened) until 70 or 80 cycles/mm. Of course there might be aliasing, which is a problem....except that aliasing looks subjectively like detail, so you might get the appearance of >100% mtf until or extinction with the D800E. The best measure of subjective sharpness is the area under the mtf curve, which in that case would be dramatically larger for the D800E than for a slide of Velvia. Even though, in theory, the Velvia can resolve to a higher resolution without aliasing. Of course you need to scan film and even a drum scanner will knock off quite a bit of mtf from the system.
Imo, the combination of reduced noise/grain and increased mtf puts state of the art digital at twice the linear resolution of film. Digital printing's vast superiority to darkroom color printing tips the tables even way further. APS-C looks like 645 to me. Full frame looks like 6x7. But I prefer how 6x7 Velvia looks to how the images from my 5D III look by a pretty enormous margin. Even though I can't explain why and even though others don't.
In terms of DR, it depends on which film (black and white negative can have easily way in excess of 10 stops, all of which are usable if you dodge and burn; Velvia has five stops maybe) and how you measure it (how much noise/grain is too much and if a soft highlight rolloff that doesn't contain recoverable detail but still looks nice counts as real DR).
In terms of color gamut, digital is more accurate but film can have a wider gamut in theory. Once scanner...doesn't matter as much, the gamut is squished. And some films have more vivid colors because the spectral sensitivity curves reject more colors than the weak bayer filters on digital SLRs.
But yeah, digital wins for a given sensor size by far. Large format film (Velvia 50, specifically) is by far my favorite in terms of aesthetics, but the price is high and you need to be very careful about light due to the limited DR and how easy it is to blow an exposure.